The invention is based on an eccentric grinder or grinding machine. An eccentric grinder is known having an eccentric shaft and a grinding disk attached nonrotatably to the eccentric shaft as well as a device for changing the grinding movement of its grinding disk with at least one fixed toothed rim, wherein an outer region of the grinding disk is arranged without connection to the rest of the parts of the grinder and is spaced axially from the latter and the grinding disk is attached to the eccentric disk in a central portion. In such a grinder, as is described in DE-OS No. 36 09 441, the toothed rims of the eccentric gear unit are fastened partly to a toothed ring and partly directly to the grinding disk. As a result, a pressure exerted on the grinding disk edge during work leads to twisting of the toothed rim arranged on the grinding disk due to the elasticity of the latter and accordingly leads to meshing difficulties in the eccentric gear unit. Moreover, the gear unit comprising six toothed rims is relatively costly.